To me they are quite similar. Example, you and I know each other from work, but we don't do things together after work. We are associates, not friends. My wife has a baby and you give me a baby gift. I would say, "Wow! Thanks Paul! You didn't have to do that!"
I could have said "You needn't have done that!" and it means exactly the same.
The first way sounds natural to me and would be the first way I would respond. I have heard the second way many times, but my guess is that it is more British than Texan.